Now that we have a feel for the set of values for which a logarithmic function is defined, we move on to graphing logarithmic functions. The family of logarithmic functions includes the parent function
along with all its transformations: shifts, stretches, compressions, and reflections.
We begin with the parent function
Because every logarithmic function of this form is the inverse of an exponential function with the form
their graphs will be reflections of each other across the line
To illustrate this, we can observe the relationship between the input and output values of
and its equivalent
in
[link].
Using the inputs and outputs from
[link] , we can build another table to observe the relationship between points on the graphs of the inverse functions
and
See
[link].
As we’d expect, the
x - and
y -coordinates are reversed for the inverse functions.
[link] shows the graph of
and
Observe the following from the graph:
has a
y -intercept at
and
has an
x - intercept at
The domain of
is the same as the range of
The range of
is the same as the domain of
Characteristics of the graph of the parent function,
f (
x ) = log
b (
x )
For any real number
and constant
we can see the following characteristics in the graph of
[link] shows how changing the base
in
can affect the graphs. Observe that the graphs compress vertically as the value of the base increases. (
Note: recall that the function
has base
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits